CFTs on Riemann Surfaces of genus $g\ge 1$

Abstract

$N$-point functions of holomorphic fields in conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulas for the 2-point function of the Virasoro field on hyperelliptic Riemann surfaces of genus $g\ge 1$. Virasoro $N$-point functions for higher $N$ are obtained inductively, and we show that they have a nice graph representation. We discuss the 3-point function with application to the $(2,5)$ minimal model.

Published version with minor corrections

References in corpus (4)

• Current Algebra on the Torus
• Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I
• Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I
• The Genus Two Partition Function for Free Bosonic and Lattice Vertex Operator Algebras

Cited by in corpus (5)

• Genus Two Zhu Theory for Vertex Operator Algebras
• Rational CFTs on Riemann surfaces
• An algebraic approach to minimal models in CFTs
• The $(2,5)$ minimal model on genus two surfaces
• CFTs on Riemann Surfaces of genus $g\ge 1$: Dependence on moduli